You're saying the little pin at the end of the rod came out of it's hole? They are designed to be two parts so you can replace the little pin when it bends or breaks. Take the rod out of the die body. On Lee's I think the rod is smooth and held by a collet. Loosen the nut on top and the rod should slip out. When you have the rod out of the die grab it tight with a pair of pliers and loosen the knob at the bottom with another pair. Don't put your pliers on the largest part of the bottom plug, that has to remain smooth. When you have loosened the plug on the bottom a turn or two you can put the decapping pin back in the hole it came out of. Make sure it is in as far as it will go. Then tighten the plug on the rod tight as you can, and put the rod back in the die body and tighten the collet that holds it tight. You will have to adjust the depth of this rod in the die so it will pop the primer out but not touch the bottom of the case.
What did you do with the instructions for the die?